Final answer:
The Ay Balwantrai Mehta Committee is associated with the subject of Local Self-Government, recommending the establishment and strengthening of the panchayati raj system in India.
Step-by-step explanation:
The committee that dealt with the subject of Local Self-Government is the Ay Balwantrai Mehta Committee. The other commissions and committees listed, such as the Kothari Commission, Veerappa Moily Committee, and Venkatachalam Commission, have been involved in various other reforms and subjects, but the Mehta Committee is historically linked with the recommendations for the establishment and strengthening of the panchayati raj system in India, enhancing local governance and community involvement.